scholarly journals A Newton Type Iterative Method with Fourth-order Convergence

2017 ◽  
Vol 12 (1) ◽  
pp. 87-95
Author(s):  
Jivandhar Jnawali
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Newton's Method ◽  
Second Order ◽  
Secant Method ◽  
Order Derivative ◽  
Single Variable ◽  
Order Convergence ◽  
Numerical Examples

The aim of this paper is to propose a fourth-order Newton type iterative method for solving nonlinear equations in a single variable. We obtained this method by combining the iterations of contra harmonic Newton’s method with secant method. The proposed method is free from second order derivative. Some numerical examples are given to illustrate the performance and to show this method’s advantage over other compared methods.Journal of the Institute of Engineering, 2016, 12 (1): 87-95

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

scholarly journals Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Gustavo Fernández-Torres ◽  
Juan Vásquez-Aquino
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
Classical Method ◽  
Multiple Roots ◽  
Order Convergence ◽  
Numerical Examples ◽  
Optimal Methods

We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.

scholarly journals Iterative Methods for Solving Nonlinear Equations with Fourth-Order Convergence

2016 ◽  
Vol 30 (2) ◽  
pp. 65-72
Author(s):  
Jivandhar Jnawali ◽  
Chet Raj Bhatta
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Fourth Order ◽  
Inverse Function ◽  
Arithmetic Mean ◽  
Second Order ◽  
Harmonic Mean ◽  
Order Convergence

In this paper, we obtain fourth order iterative method for solving nonlinear equations by combining arithmetic mean Newton method, harmonic mean Newton method and midpoint Newton method uniquely. Also, some variant of Newton type methods based on inverse function have been developed. These methods are free from second order derivatives.

scholarly journals Eighteenth Order Convergent Method for Solving Non-Linear Equations

2017 ◽  
Vol 10 (1) ◽  
pp. 144-150 ◽  
Author(s):  
V.B Vatti ◽  
Ramadevi Sri ◽  
M.S Mylapalli
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Equations ◽  
Subject Classification ◽  
Order Convergence ◽  
Numerical Examples ◽  
Convergent Method ◽  
Non Linear Equations

In this paper, we suggest and discuss an iterative method for solving nonlinear equations of the type f(x)=0 having eighteenth order convergence. This new technique based on Newton’s method and extrapolated Newton’s method. This method is compared with the existing ones through some numerical examples to exhibit its superiority. AMS Subject Classification: 41A25, 65K05, 65H05.

scholarly journals A fourth order method for finding a simple root of univariate function

2015 ◽  
Vol 34 (2) ◽  
pp. 197-211
Author(s):  
D. Sbibih ◽  
Abdelhafid Serghini ◽  
A. Tijini ◽  
A. Zidna
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Simple Root ◽  
Newton's Method ◽  
Order Method ◽  
Numerical Examples ◽  
Quadratic Interpolation ◽  
Univariate Function ◽  
Fourth Order Method

In this paper, we describe an iterative method for approximating asimple zero $z$ of a real defined function. This method is aessentially based on the idea to extend Newton's method to be theinverse quadratic interpolation. We prove that for a sufficientlysmooth function $f$ in a neighborhood of $z$ the order of theconvergence is quartic. Using Mathematica with its high precisioncompatibility, we present some numerical examples to confirm thetheoretical results and to compare our method with the others givenin the literature.

scholarly journals Some novel Newton-type methods for solving nonlinear equations

2019 ◽  
Vol 38 (3) ◽  
pp. 111-123
Author(s):  
Morteza Bisheh-Niasar ◽  
Abbas Saadatmandi
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Basins Of Attraction ◽  
Sixth Order ◽  
New Method ◽  
Order Convergence ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Newton Iterative Method

The aim of this paper is to present a new nonstandard Newton iterative method for solving nonlinear equations. The convergence of the proposed method is proved and it is shown that the new method has cubic convergence. Furthermore, two new multi-point methods with sixth-order convergence, based on the introduced method, are presented. Also, we describe the basins of attraction for these methods. Finally, some numerical examples are given to show the performance of our methods by comparing with some other methods available in the literature

A New SPH Iterative Method for Solving Nonlinear Equations

2019 ◽  
Vol 17 (01) ◽  
pp. 1843005 ◽  
Author(s):  
Rahmatjan Imin ◽  
Ahmatjan Iminjan
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Basic Principle ◽  
Newton’S Method ◽  
Newton's Method ◽  
Quadratic Convergence ◽  
Taylor Series Expansion ◽  
Numerical Examples ◽  
First Order ◽  
Kernel Approximation

In this paper, based on the basic principle of the SPH method’s kernel approximation, a new kernel approximation was constructed to compute first-order derivative through Taylor series expansion. Derivative in Newton’s method was replaced to propose a new SPH iterative method for solving nonlinear equations. The advantage of this method is that it does not require any evaluation of derivatives, which overcame the shortcoming of Newton’s method. Quadratic convergence of new method was proved and a variety of numerical examples were given to illustrate that the method has the same computational efficiency as Newton’s method.

scholarly journals A New Variant of Newton’s Method With Fourth–Order Convergence

2016 ◽  
Vol 21 (1) ◽  
pp. 86-89
Author(s):  
Jivandhar Jnawali ◽  
Chet Raj Bhatta
Keyword(s):  
Iterative Method ◽  
Linear Combination ◽  
Newton Method ◽  
Fourth Order ◽  
Inverse Function ◽  
Order Convergence ◽  
Numerical Examples ◽  
New Variant ◽  
Indefinite Integral ◽  
New Iterative Method

In this paper, we present new iterative method for solving nonlinear equations with fourth-order convergence. This method is free from second and higher order derivatives. We find this iterative method by using Newton's theorem for inverse function and approximating the indefinite integral in Newton's theorem by the linear combination of harmonic mean rule and Wang formula. Numerical examples show that the new method competes with Newton method, Weerakoon - Fernando method and Wang method.Journal of Institute of Science and TechnologyVol. 21, No. 1, 2016, page :86-89

A New Iterative Method with Sixth-Order Convergence for Solving Nonlinear Equations

2012 ◽  
Vol 542-543 ◽  
pp. 1019-1022
Author(s):  
Han Li
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Efficiency Index ◽  
Order Convergence ◽  
Second Derivatives ◽  
New Iterative Method ◽  
Better Than

In this paper, we present and analyze a new iterative method for solving nonlinear equations. It is proved that the method is six-order convergent. The algorithm is free from second derivatives, and it requires three evaluations of the functions and two evaluations of derivatives in each iteration. The efficiency index of the presented method is 1.431 which is better than that of classical Newton’s method 1.414. Some numerical experiments illustrate that the proposed method is more efficient and performs better than classical Newton's method and some other methods.

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

Sign in / Sign up

Export Citation Format

Share Document